Airline

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shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sat Feb 20, 2010 12:59 pm

An airline has a certain free luggage allowance and charges for excess luggage at a fixed rate per kg. Two passengers, Raja and have 60 kg of luggage between them, and are charged Rs. 1200 and Rs. 2400 respectively for excess luggage. Hand the entire luggage to one of them, the excess luggage charge would have been Rs. 5400.

What is the free luggage allowance?
A) 10Kg
B) 15Kg
C) 20Kg
D) 25Kg
E) 30Kg

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Source: Beat The GMAT — Problem Solving | Sat Feb 20, 2010 12:59 pm

gmattarget700: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Mon Jan 05, 2009 11:10 pm; Thanked: 2 times

by gmattarget700 » Sat Feb 20, 2010 2:37 pm

with my very rough paper work, with just the agenda/attempt to finding the correct answer - it seems answer should be B

gmattarget700: Senior | Next Rank: 100 Posts; Posts: 67; Joined: Mon Jan 05, 2009 11:10 pm; Thanked: 2 times

by gmattarget700 » Sat Feb 20, 2010 2:38 pm

post the correct answer

shashank.ism: Legendary Member; Posts: 1022; Joined: Mon Jul 20, 2009 11:49 pmFollowed by: 2 members; Location: Gandhinagar; Thanked: 41 times

by shashank.ism » Sat Feb 20, 2010 11:45 pm

gmattarget700 wrote:with my very rough paper work, with just the agenda/attempt to finding the correct answer - it seems answer should be B

you could have takena snap of ur rough work and posted the soln here..
oreither could have written the ans..Well correct ans is B..

Let the free luggage allowance be x kg. The data is as below.

Free Allowance : Raja (x) Praja (x)

Excess : Raja ( a – x ) Praja (60 – a – x)
Praja pays Rs.2400 for 60 – a – x
Raja pays Rs.1200 for a – x
∴ 60 – a – x = 2(a – x)
⇒ 60 + x = 3a -----------------(i)
If the entire luggage belonged to, say Praja, he would have
to pay Rs.5400.

∴
(60 -a-ax)/(60-x)=2400/5400 = 4/9
⇒ 540 – 9a – 9x = 240 – 4x

⇒ 300 – 5x = 9a -------------(ii)
From (i) and (ii) x = 15 and a = 25
∴ Praja’s luggage is 60 – 25 = 35 kg and the free allowance in 15 kg.

[spoiler]Hence (B)[/spoiler]

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